The family of a volunteer firefighter who died a hero’s death on Sept. 11 reclaimed a priceless memento yesterday – the gold watch Glenn Winuk was wearing when he rushed into the south tower to save lives.

The handsome Swiss timepiece had stopped on the 12th day of the month – perhaps Sept. 12 – the time fixed at 12:55.

“It kind of gets your heart going knowing this is what he was wearing when he died,” said his brother Jay, standing outside One Police Plaza after receiving the keepsake. “Now we finally have it back in our family. What a long, strange trip it’s been.”

Glenn’s remains were found in March 2002, but not many of the belongings found with him were salvageable.

So his family buried the 40-year-old with other symbols of a life well lived – old Cub Scout mementos, a hat from his days as volunteer fire commissioner in Jericho, L.I., and a couple of law books he used as a partner at Holland & Knight LLP near the WTC.

But “we always felt terrible we didn’t have anything of substance he was carrying that day,” said Jay, 47. And the watch, bought for $1,800 a decade ago on a trip to Las Vegas with buddies, was particularly important because “it represented a happy time for him.”

The hardworking lawyer rarely took time for himself. In his spare time, he volunteered as a firefighter and an EMT, and was constantly taking courses to better his skills – including certification in evacuating collapsing buildings.

So it was only natural that he responded to the attacks by borrowing equipment and racing up Dey Street to the towers, Jay said.

A year ago, Jay was shocked to receive a phone call from the city Medical Examiner’s Office, saying a valuable Swiss watch had been found at Ground Zero – and it matched the description the family had given to authorities in the days after the tragedy.

It seemed like a match, but finding proof was another matter. Jay sent authorities a photo of his brother wearing the watch, but NYPD officials, who were holding the piece, demanded better evidence.

After stressful weeks of combing through his brother’s belongings, Jay finally found a copy of the warranty, including the serial number.

It was the same watch.

“There was such a great sense of relief to me,” Jay recalled.

Yesterday, a nervous, emotional Jay went to Police Headquarters in lower Manhattan to claim one last piece of his brother’s memory.

“I only know it from pictures and descriptions, but it seems familiar,” he said, turning the 18-carat gold Ebel Swiss watch, now worth $2,950, over in his hands.